Theor Ecol
DOI 10.1007/s12080-011-0138-9
ORIGINAL PAPER
Diversity emerging: from competitive exclusion
to neutral coexistence in ecosystems
Juan E. Keymer · Miguel A. Fuentes ·
Pablo A. Marquet
Received: 15 February 2011 / Accepted: 22 August 2011
© Springer Science+Business Media B.V. 2011
Abstract In this communication, we present a unifying
framework to understand the emergence and maintenance of diversity in ecological systems. We do this by
developing a deterministic population model including
density-dependent limitation in resources and available
space. Our model shows that competitive exclusion and
neutral coexistence represent different regimes of the
same adaptive dynamics suggesting that neutrality is
the general result of an adaptive process in a finite
habitat with limited energetic resources. Our model explains the emergence of biodiversity through mutation
and its maintenance through neutrality. We show that
this framework provides the theoretical foundations to
Electronic supplementary material The online version
of this article (doi:10.1007/s12080-011-0138-9) contains
supplementary material, which is available to
authorized users.
J. E. Keymer
Department of Bionanoscience,
Kavli Institute of Nanoscience,
Delft University of Technology,
Lorentzweg 1, 2600 Delft, The Netherlands
e-mail: J.E.KeymerVergara@tudelft.nl
M. A. Fuentes
Consejo Nacional de Investigaciones Científicas y Técnicas,
Statistical and Interdisciplinary Physics Group,
Centro Atómico Bariloche and Instituto Balseiro,
8400 Bariloche, Argentina
e-mail: fuentesm@santafe.edu
M. A. Fuentes · P. A. Marquet
Center for Advanced Studies
in Ecology and Biodiversity (CASEB),
Pontificia Universidad Católica de Chile,
Santiago 6513677, Chile
understand the emergence and maintenance of diversity in microbial ecosystems.
Keywords Emergence · Diversity ·
Adaptive dynamics · Competition · Neutrality
Introduction
The processes by which diversity is generated and maintained in ecosystems are at the core of ecological inquiry. And yet, it is striking that we do not have a simple
and general quantitative theory of biodiversity generation and maintenance, notwithstanding several recent
efforts in this direction (Hubbell 1997, 2001; Huisman
et al. 2001; Allen et al. 2002; Brown et al. 2004). One of
the impediments for achieving a general theory is the
fondness of ecologists with complex ecological systems
M. A. Fuentes
Facultad de Gobierno, Universidad del Desarrollo,
Santiago, Chile
P. A. Marquet (B)
Departamento de Ecología,
Facultad de Ciencias Biológicas,
Pontificia Universidad Católica de Chile,
Santiago 6513677, Chile
e-mail: pmarquet@bio.puc.cl
P. A. Marquet
Instituto de Ecología y Biodiversidad (IEB),
Casilla 653, Santiago, Chile
P. A. Marquet
Santa Fe Institute, 1399 Hyde Park Road,
Santa Fe, NM 87501, USA
Theor Ecol
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Density
such as tropical forests and coral reefs, as if a general
theory of biodiversity should be easier to achieve under the inspiration of highly diverse ecosystems, e.g.,
Volkov et al. (2007). In this context, it is not surprising
that most theories, such as neutral and stochastic theories as well as niche and resource-based ones (Hubbell
1997, 2001; Caswell 1976; Tilman 1982, 1994; Chesson
2000; Tilman and Pacala 1993) emphasize biodiversity
maintenance but lack a formal treatment of biodiversity
generation. In contrast, simple ecosystems represented
by cultured bacteria populations, by virtue of their
large population size, short generation time, and easy
of experimentation, have gradually taken a leading role
in fostering our understanding of the processes underlying the emergence of diversity (Rainey et al. 2000;
Seehausen 2007).
It is well known that cultures inoculated with an
isogenic strain of bacteria gradually give rise to diversity, or genetic polymorphism in the form of mutant
strains, even in the absence of environmental heterogeneity, e.g., Zambrano et al. (1993), Rosenzweig et al.
(1994), Riley et al. (2001), and Maharjan et al. (2006).
Typically, population takeovers by fitter mutants (i.e.,
periodic selection, Atwood et al. 1951) have been the
rule in chemostat (Novick and Szilard 1951; Helling
et al. 1987) and in serial transfer batch cultures (Lenski
and Travisano 1994). Periodic selection is closely associated with competitive exclusion and thus with the
winning and complete takeover by the fittest mutant.
Chemostats and sequential transfer experiments, however, may not adequately represent all extant diversity due to potential losses accrued by dilution (as in
chemostats) or by transferring only a sample of the
population to a fresh medium (as in sequential transfer lines). Furthermore, the usual culturing conditions
might not adequately represent the stress associated to
low resource levels and intense competition, which are
common in natural microbial ecosystems (Morita 1988,
1997; Zinser and Kolter 2004; Finkel 2006), and the
increased mutation rate and diversity that these may
trigger (Bjedov et al. 2003; Tenaillon et al. 2004). In
fact, experimental results on bacterial evolution under
stress conditions (i.e. batch cultures with prolonged
starvation, Zambrano et al. 1993; Finkel and Kolter
1999; Zinzer and Kolter 1999, 2000) not only resulted
in the commonly observed periodic selection but also
in high levels of strain diversity (see Fig. 1). Interestingly, while it was early recognized that these result
could hold important insights for understanding the
mechanisms underlying the emergence of diversity in
ecosystems (Finkel 2006; Finkel and Kolter 1999), see
reviews in Zinser and Kolter (2004), no theory has
explained them as yet.
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200
250
300
350
400
450
time (days)
Fig. 1 Coexistence of different colony morphotypes, indicated by
colors, during long-term incubation of an initially isogenic strain
of E. coli. From data in Fig. 4 of Finkel and Kolter (1999)
In this paper, we present a general model to understanding the emergence and maintenance of diversity in
ecological systems, which uses exploitative competition
for resources (Tilman 1982; Hansen and Hubbell 1980;
Finkel et al. 2000), in an adaptive dynamics framework.
Our central tenet is that diversity is driven by two
density-dependent mechanisms: spatial constraints to
individual packing and resource constraints to individual persistence and reproduction. Our model shows
that the interaction between these two limiting factors underlies biodiversity generation through mutation (innovation) and maintenance through neutrality.
Furthermore, we show that this framework provides
the theoretical foundations for understanding the
emergence and maintenance of diversity in microbial
ecosystems.
The model
Following Keymer et al. (2006), we consider a logistic
Verhulst-type growth scenario
d
φ = rφ(1 − φ),
dt
(1)
where φ is the biomass of the bacterial strain. The
logistic term in this equation represents the effect of the
finiteness of the habitat wherein resources and biomass
are contained, such that even if resources to provision
further growth are present, this will not occur because
of lack of space to put new biomass.
Theor Ecol
We assume that the growth rate r depends on the
quality of the habitat ω, 0 ≤ ω ≤ 1, which specifies the
amount of local resources that can be turned into new
biomass. Then,
r(ω) = f ω − m,
(2)
with f and m being fecundity and mortality rates,
respectively. Habitat-quality dynamics is modeled as
d
ω = F − C,
dt
(3)
where F and C are the supply and consumption rates
of resources, respectively. We model them using the
following functional forms
F = λ(1 − ω), C = φω f,
(4)
where λ is the supply rate of resources while represents the amount of nutrients per unit biomass. This
formulation comes from the resource-based model introduced by Roughgarden (1998).
The scenario we are interested corresponds to a
strain growing in a habitat that do not receive any external supply of resources after colonization, as in Kolter’s
bacterial batch culture, but where new resources
become available from the inside as a result of biomass decomposition or as by-products of the metabolic
activity of bacteria, through the process known as
cross-feeding, e.g., Helling et al. (1987). Notice that,
in our model, negative density dependence acts upon
fecundity as well as mortality, such that when biomass
saturates the habitat, reaching stationary phase, both
rates tend to zero. This is a well-known phenomena
in bacterial cultures, where upon reaching stationaryphase bacterial cells cease to grow and divide, entering
metabolic arrest or a spore-like physiological state; surviving for long periods of time with minimal metabolic
activity (Kolter et al. 1993; Vulić and Kolter 2001).
By using Eqs. 1 and 3 we represent such ecology as
d
φ = ( f ω − m)φ(1 − φ),
dt
(5)
d
ω = λ(1 − ω) − φω f.
dt
(6)
This system has three possible long-term behaviors
(indicated with supra-indices):
–
Extinction. In this scenario, biomass goes to zero
φ̂ 0 = 0. However, due to the resources supplied
by the biomass through its metabolic activity, the
habitat quality goes to its maximum ω̂0 = 1 (i.e., the
habitat is saturated with resources accumulated as
a by-product of metabolism).
–
–
Bottom-up regulated. Here, we have that biomass in the long-term goes to φ̂ 1/2 = λ(R − 1)/( f ),
where R = 1/ω∗ and ω∗ = m/ f while habitat quality goes to ω̂1/2 = ω∗ .
Top-down regulated. Here, biomass reach a maximum saturating the habitat, φ̂ 1 = 1 while habitat
quality goes to ω̂1 = H, with H = λ/(λ + f ).
If we normalize time as 1/ f , we arrive to the following simplified equations
d
φ = ω − ω∗ φ(1 − φ),
dτ
(7)
d
λ
ω = (1 − ω) − φω.
dτ
f
(8)
Here, we assume that > 0 and the resource recycling
through cross-feeding λ > 0 are both fixed, and that the
trait ω∗ (ω∗ = m/ f ) is subject to an adaptive dynamics,
whereby new mutant strategies characterized by slight
changes in ω∗ continuously arise in the population
(see next section below).
As before there are three equilibrium points. The
extinction equilibrium is stable when a strategy is
characterized by ω∗ > 1 (i.e., mortality is higher than
fecundity). The bottom-up regulated equilibrium is stable for strategies satisfying H < ω∗ < 1. As strategies
with smaller ω∗ are considered, the top-down regulated
equilibrium will kick in. This last equilibrium, ω̂1 ≡ H,
is stable when 0 ≤ ω∗ ≤ H that is, when resources are
no longer constraining biomass accumulation. At this
point, the finite nature of the habitat becomes a strong
constraint upon new biomass, as there is no more free
volume to put the new biomass that can be made.
Here, habitat quality is determined by the parameters
λ and .
In general, the important parameters for the stability of the system are ω∗ , which measures the ratio
between mortality and fecundity, and f/λ, that appears in the threshold H. Figure 2 shows the stationary
solutions for the equilibrium biomass φ̂ and their stability properties.
To understand the dynamic implications of this phenomenon, in an environment where new mutants may
continually arise, we now turn to an adaptive dynamics
framework (e.g. Metz et al. 1996; Diekmann 2004).
Adaptive dynamics
An adaptive dynamics in a continuous trait space is
particularly suited for uncovering the most likely course
that evolution would follow under the conditions
Theor Ecol
In both cases, we consider the fate (invasion exponent) of a rare strategy ωμ∗ , defined by
1 d
φμ = ωr∗ − ωμ∗ 1 − φ̂r ,
S ≡ Sωr∗ ωμ∗ ≡
φμ dτ
Fig. 2 Equilibrium states for the dynamics of biomass in a patch
with resource renewal. Continuous and dashed lines represent
stable and unstable equilibria, respectively
(9)
within a background environment characterized by an
equilibrium resident strategy ωr∗ resting at its (stable)
equilibrium point φ̂r (see Online Resource
1/2 1). The particular equilibrium point φ̂r or φ̂r1 to consider for the resident equilibrium density φ̂r , depends
on what region of the strategy space is the resident
trait ωr∗ at.
Case I, H < ωr∗ < 1. Corresponds to the bottom1/2
up regulated equilibrium. Thus, φ̂r ought to be considered. For this case the invasion exponent corresponds to:
(10)
S = ωr∗ − ωμ∗ 1 − φ̂r1/2 ,
and the fitness gradient for the mutants looks like
specified by our deterministic model (Metz et al. 1996;
Diekmann 2004).
Two of the fundamental ideas of adaptive dynamics
are: (1) that a resident population, φr , can be assumed
at equilibrium φr ≡ φ̂r when new mutants, φμ , appear
and that (2) the fate of these mutants can be inferred
from their growth rate when rare (i.e., at the beginning
of the invasion) in the environment occupied by the
resident, this per capita rate is defined below and it is
known as the invasion exponent S or invasion fitness
(Metz et al. 1992). Finally, we calculate the selection
gradient S which gives a local description of the fitness
landscape experienced by an emerging (rare) mutant,
indexed by μ, in the context of an equilibrium resident
population, indexed by r (Diekmann 2004), under the
ecological conditions described by Eqs. 7 and 8.
Notice that applying adaptive dynamics theory for
this case is straightforward (see Online Resource 1),
and we only need to consider the change in attractor
stability when the evolving trait crosses a critical boundary, triggering a stability change in the fixed points for
the resident population. In general, we need to perform
an invasion analysis for each of the three regions of
the parameters space, which correspond to attractors
φ̂ 0 , φ̂ 1/2 , or φ̂ 1 .
Since in order to evolve, strategies must actually
exist, we know that the relevant problem only involve
strategies in the region 0 ≤ ω∗ < 1. So, only two cases
must be considered as our equilibrium resident pop1/2
ulation φ̂r : (a) bottom-up φ̂r scenario for strategies
H < ω∗ < 1, and (b) a top-down φ̂r1 scenario for strategies 0 ≤ ω∗ ≤ H.
S ≡
d
Sω∗ = φ̂r1/2 − 1,
dωμ∗ r
(11)
which is negative, S < 0 since φ̂r < 1. Thus, there
is a directional evolution of the trait ω∗ to the left
(smaller values) in strategy space until it reaches strategies within the next region, to the left of ωc∗ ≡ H.
Case II, 0 ≤ ωr∗ ≤ H. Corresponds to strategies that
saturate available space. For these strategies, the equilibrium point to consider corresponds to the top-down
1/2
Fig. 3 Selection gradient as a function of ω∗ . The threshold value
H, is where the top-down solution becomes stable. This is the
boundary at which a neutral ecology emerges
Theor Ecol
regulated one φ̂r ≡ φ̂r1 = 1. In this case, the invasion
exponent of any new mutant vanishes, since
S = ωr∗ − ωμ∗ 1 − φ̂r1 = 0.
(12)
A plot of the selection gradient, S , associated to
the bottom-up equilibrium is negative, implying a steep
fitness landscape where new mutant strategies carry
a selective advantage over the resident one, and thus
can invade the population (Fig. 3). However, as soon
as the bottom-up regulated equilibrium is reached the
invasion exponent of any new mutant vanishes and as
a consequence the fitness gradient becomes flat and a
neutral ecology emerges, where any possible mutant
that arises is ecologically equivalent.
Discussion
Ever since the struggle for existence and the competitive exclusion principle, diversity, and more generally
coexistence, has been a vexing problem in ecology and
evolutionary biology (Muller 1932).
Spontaneous beneficial mutations are the fundamental source for adaptation, innovation and diversity. In
asexual populations, however, mutants better endowed
with fitness will tend to replace other mutants through
periodic selection or clonal interference (Gerrish and
Lenski 1998; Hegreness et al. 2006) putting a ceiling
to diversity at its lowest value. Several hypothesis and
models based on resource partitioning, cross-feeding,
demographic trade-offs, and frequency-dependent selection have envisioned realistic scenarios for fitness
equalization and thus coexistence and microbial diversity (Rosenzweig et al. 1994; Helling et al. 1987; Turner
et al. 1996; Rozen and Lenski 2000; Czárán et al. 2002;
Kerr et al. 2002; Friesen et al. 2004) with the recently
proposed neutral theory (Hubbell 2001) representing
an extreme explanation, which assumes that individuals live in a flat fitness landscape, such that diversity
is driven by mutation, dispersal and ecological drift
(Hubbell 2001).
Our model builds on resource-based competition,
which when taking place in a finite habitat gives way
to neutrality as a result. It unifies both approaches
by assuming that species, in addition of being limited
by resources (our bottom-up regulation) also face the
geometric constraints imposed by the finiteness of their
habitats (our top-down constraint), when packing biomass into individuals. The combined action of these
density-dependent effects gives raise to an adaptive
dynamics characterized by a transition from fitness-
mediated competitive exclusion to neutrality. The later
arises when the habitat patch is saturated with biomass,
such that any new favorable mutation, let say for using a different amino acid as a source of carbon, is
not better endowed that any other one. This result is
equivalent to the biotic saturation or zero-sum assumption in first-generation neutral models (Hubbell 2001).
In this regard, what our model shows is that space
limitation is sufficient to put the dynamics of species
diversity, as driven by competition and speciation, into
a flat fitness landscape or neutral regime. In this sense,
space limitation provides a hard boundary that equalizes fitness by not allowing room for new and better
adapted varieties. Recent neutral models have relaxed
the zero-sum assumption but have retained the neutrality or symmetry assumption that all individuals behave
the same under the same intraspecific circumstances
(Alonso et al. 2008; Haegeman and Etienne 2008) in
order to derive observables such as abundance distributions. Our model is fundamentally different in this
regard, as we do not assume neutrality but arrive to it
through an adaptive dynamics driven by food and space
limitation. In this sense, it is similar to recent models
where neutrality is the result of ecological equivalence
driven by mechanisms that equalize fitness (e.g., lifehistory trade-offs and dispersal limitation) and therefore allows for the coexistence of different types in
competitive communities (Bonsall et al. 2004; Gravel
et al. 2006; Scheffer and van Nes 2006; Doncaster 2009).
It differs from them, however, in that the main forces
driving diversity and coexistence are limitation for energy resources and space, while not assuming species
specific trade-offs in competitive abilities or dispersal.
It remains to be explored how the neutral dynamics
resulting from our model compares with predictions
derived from neutral models, such as species abundance distributions and other observables (Etienne and
Alonso 2005).
Our model captures the essential features of the
long-term starvation experiments that inspired its development (Finkel and Kolter 1999), that is, waves
of successive takeovers or periodic selection followed
by coexistence of multiple mutants. The mechanisms
underlying the emergence of progressively fitter mutants that get a growth advantage in stationary phase
(i.e., that posses the GASP phenotype), with a competitive advantage to mutants of order n + 1 over those of
lower order (i.e., that emerged earlier in the population), is related to several GASP mutations (Zambrano
et al. 1993; Zinser and Kolter 2004; Zinzer and Kolter
1999, 2000) which, among other things, result in an
increased ability to catabolize one or more amino acids
as a source of carbon and energy.
Theor Ecol
The ecological scenario of a batch cultured population of Escherichia coli entering GASP (around 10 days
after initial inoculation) is characterized by the nearly
exhaustion of carbon sources from where to extract
energy, unless new mutations allow for the use of
the only carbon sources available; organic compounds
derived from metabolic activity and those trapped in
bacterial biomass. Once a GASP mutant arises, it will
take over the population only to be replaced by mutants more efficient in using other available sources
of carbon, scavenging for the carbon retained in the
debris of dead bacterial cells or both. Indeed, in Zinzer
and Kolter (1999) it is shown that GASP mutations
act additively, conferring faster growth on mixtures of
amino acids. During the neutral phase, all resources
have been transformed to bacterial biomass, which becomes the resource itself. During this stage, it is possible to hypothesize that fitness will no longer increase
after all the mutations required to use available amino
acids have occurred, putting the dynamics onto a flat
fitness landscape where bacterial biomass becomes the
consumer and the resource. In this sense, our densitydependent constraint linked to habitat size somehow
impose a limit to adaptation. It is also possible that
successive strains are engaged in niche construction
dynamics (Odling-Smee et al. 2003) such that although
they may exclude each other, the winner always change
the selective environment to favor a new variety until
no further construction is possible. The functioning of
this neutral ecosystem will slowly degrade in time as a
consequence of energy dissipation, causing biomass to
decrease. So far, long-term starvation experiments of
bacteria have lasted for more than 5 years, and although
there is evidence of a biomass decrease, see Fig. 1 in
Finkel (2006), further analyses are necessary.
Finally, it is important to point out that resource and
geometric constraints due to habitat finiteness are simple but fundamental ubiquitous characteristics of life,
present since its emergence on earth. The model proposed herein derives how under these constraints competitive exclusion, diversity and neutrality can arise.
Furthermore, our model suggests that neutrality may
not only be an assumption for mathematical tractability
or a null model for ecological understanding (Hubbell
2001; Caswell 1976; Alonso et al. 2006) but the general
results of an adaptive process in a finite habitat with
limited resources.
Acknowledgments We thank Hans Metz, David Krakauer,
Sander van Doorn, Elhanan Borenstein, Geoffrey West, and
three anonymous reviewers for constructive criticisms, insights,
and discussions. PAM acknowledges support from a John Simon
Guggeheim Felowship and grants FONDAP-FONDECYT 15010001, ICM P05-02, Basal Financing Program CONICYT-PFB-
023, the working group Unifying theories in ecology at the
National Center for Ecological Analysis and Synthesis, a Center
funded by NSF (grant no. DEB-0072909), the University of
California, and the Santa Barbara campus, and SFI International
Program. JEK acknowledges TU Delft for startup support.
References
Allen AP, Brown JH, Gillooly JF (2002) Global biodiversity,
biochemical kinetics, and the energetic-equivalence rule.
Science 297:1545–1548
Alonso D, Etienne RS, McKane J (2006) The merits of neutral
theory. Trends Ecol Evol 21:451–457
Alonso D, Ostling A, Etienne RS (2008) The implicit assumption
of symmetry and the species abundance distribution. Ecol
Lett 11:93–105
Atwood KC, Schneider LK, Ryan FJ (1951) Periodic selection in
Escherichia coli. Proc Natl Acad Sci USA 37:146–155
Bjedov I, Tenaillon O, Grard B, Souza V, Denamur E, Radman
M, Taddei F, Matic I (2003) Stress-induced mutagenesis in
bacteria. Science 300:1404–1409
Bonsall MB, Jansen VAA, Hassell MP (2004) Life history tradeoffs assemble ecological guilds. Science 306:111–114
Brown JH, Gillooly JF, Allen AP, Savage VM, West GB
(2004) Toward a metabolic theory of ecology. Ecology
85:1771–1789
Caswell H (1976) Community structure: a neutral model analysis.
Ecol Monogr 46:327–354
Chesson PL (2000) Mechanisms of maintenance of species diversity. Annu Rev Ecol Syst 31:343–366
Czárán TL, Hoekstra RF, Pagie L (2002) Chemical warfare
between microbes promotes biodiversity. Proc Natl Acad Sci
USA 99:786–790
Diekmann O (2004) A beginner’s guide to adaptive dynamics.
Banach Cent Publ 63:47–86
Doncaster CP (2009) Ecological equivalence: a realistic assumption for niche theory as a testable alternative to neutral theory. PLoS One 4(10):e7460
Etienne RS, Alonso D (2005) A dispersal-limited sampling theory for species and alleles. Ecol Lett 8:1147–1156. Erratum
in Ecol Lett 9:500
Finkel SE (2006) Long-term survival during stationary phase:
evolution and the GASP phenotype. Nat Rev Microbiol
4:113–120
Finkel SE, Kolter R (1999) Evolution of microbial diversity during prolonged starvation. Proc Natl Acad Sci USA 96:4023–
4027
Finkel SE, Zinser E, Kolter R (2000) Long-term survival and evolution in the stationary phase. In: Storz G, Hengge-Aronis
R (eds) Bacterial stress responses. ASM Press, Washington
DC, pp 231–238
Friesen ML, Saxer G, Travisano M, Doebeli M (2004) Experimental evidence for sympatric ecological diversification
due to frequency-dependent competition in Escherichia coli.
Evolution 58:245–260
Gerrish PJ, Lenski RE (1998) The fate of competing beneficial
mutations in an asexual population. Genetica 102/103:127–
144
Gravel D, Canham CD, Beaudet M, Messier C (2006) Reconciling niche and neutrality: the continuum hypothesis. Ecol
Lett 9:399–406
Haegeman B, Etienne RS (2008) Relaxing the zero-sum assumption in neutral biodiversity theory. J Theor Biol 252:288–294
Theor Ecol
Hansen SR, Hubbell SP (1980) Single-nutrient microbial competition: qualitative agreement between experimental and
theoretically forecast outcomes. Science 207:1491–1493
Hegreness M, Shoresh N, Hartl D, Kishony R (2006) An equivalence principle for the incorporation of favorable mutations
in asexual populations. Science 311:1615–1617
Helling RB, Vargas CN, Adams J (1987) Evolution of
Escherichia coli during growth in a constant environment.
Genetics 116:349–358
Hubbell SP (1997) A unified theory of biogeography and relative
species abundance and its application to tropical rainforests
and coral reefs. Coral Reefs 16:S9–S21
Hubbell SP (2001) The unified neutral theory of biodiversity and
biogegraphy. Princeton University Press, Princeton
Huisman J, Johansson AM, Folmer EO, Weissing FJ (2001) Towards an solution of the plankton paradox: the importance
of physiology and life history. Ecol Lett 4:408–411
Kerr B, Riley MA, Feldman MW, Bohannan JM (2002) Local
dispersal promotes biodiversity in a real-life game of rockpaper-scissor. Nature 418:171–174
Keymer JE, Galajda P, Muldoon C, Park S, Austin RH (2006)
Bacterial metapopulations in nanofabricated landscapes.
Proc Natl Acad Sci USA 103:17290–17295
Kolter R, Siegele DA, Tormo A (1993) The stationary phase
of the bacterial life cicle. Annu Rev Microbiol (USA)
47:855–874
Lenski RE, Travisano M (1994) Dynamics of adaptation and diversification: a 10,000-generation experiment with bacterial
populations. Proc Natl Acad Sci USA 91:6808–6814
Maharjan R, Seeto S, Notley-McRobb L, Ferenci T (2006)
Clonal adaptive radiation in a constant environment. Science
313:514–517
Metz JAJ, Geritz SAH, Nisbet RM (1992) How should we define
‘fitness’ for general ecological scenarios? TREE 7:198–202
Metz JAJ, Geritz SAH, Meszena G, Jacobs FJA, Van
Heerwaarden JS (1996) Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. In: van Strien SJ, Verduyn Lunel SM (eds) Stochastic
and spatial structures of dynamical systems. North Holland,
Amsterdam, pp 183–231
Morita RY (1997) Bacteria in oligotrophic environments:
starvation-survival lifestyle. Chapman & Hall, London
Morita RY (1988) Bioavailability of energy and its relationship
to growth and starvation survival in nature. Can J Microbiol
34:436–441
Muller HJ (1932) Some genetic aspects of sex. Am Nat 68:118–
138
Novick A, Szilard L (1951) Experiments with the chemostat on
spontaneous mutations of bacteria. Proc Natl Acad Sci USA
36:708–719
Odling-Smee FJ, Laland KN, Feldman MW (2003) Niche construction: the neglected process in evolution. In: Monographs in population biology. Princeton University Press,
Princeton
Rainey PB, Buckling A, Kassen R, Travisano M (2000) The
emergence and maintenance of diversity: insights from experimental bacterial populations. Trends Ecol Evol 15:243–
247
Riley MS, Cooper VS, Lenski RE, Forney LJ, Marsh TL (2001)
Rapid phenotypic change and diversification of a soil bacterium during 1,000 generations of experimental evolution.
Microbiology 147:995–1006
Roughgarden JR (1998) Primer of ecological theory. PrenticeHall, Englewood Cliffs
Rozen DE, Lenski RE (2000) Long-term experimental evolution
in Escherichia coli. VIII. Dynamics of a balanced polymorphism. Am Nat 155:24–35
Rosenzweig RF, Sharp RR, Treves DS, Adams J (1994)
Microbial evolution in a simple unstructured environment:
genetic differentiation in Escherichia coli. Genetics 137:903–
917
Scheffer M, van Nes EH (2006) Self-organized similarity, the
evolutionary emergence of groups of similar species. Proc
Natl Acad Sci USA 103:6230–6235
Seehausen O (2007) Chance, historical contingency and ecological determinism jointly determine the rate of adaptive radiation. Heredity 99:361–363
Tenaillon O, Denamur E, Matic I (2004) Evolutionary significance of stress-induced mutagenesis in bacteria. Trends
Microbiol 12:264–270
Tilman D (1982) Resource competition and community structure. In: Monographs in population biology. Princeton University Press, Princeton
Tilman D (1994) Competition and biodiversity in spatially structured habitats. Ecology 75:2–16
Tilman D, Pacala S (1993) The maintenance of species richness in
plant communities. In: Ricklefs RE, Schluter D (eds) Species
diversity in ecological communities. University of Chicago
Press, Chicago, pp 13–25
Turner PE, Souza V, Lenski RE (1996) Test of ecological mechanisms promoting the stable coexistence of two bacterial
genotypes. Ecology 77:2119–2129
Volkov I, Banavar JR, Hubbell SO, Maritan A (2007) Patterns
of relative species abundance in rainforests and coral reefs.
Nature 450:45–49
Vulić M, Kolter R (2001) Evolutionary cheating in Escherichia
coli stationary phase cultures. Genetics (USA) 158:519–526
Zambrano MM, Siegele DA, Almirón M, Tormo A, Kolter R
(1993) Microbial competition: Escherichia coli mutants that
take over stationary phase cultures. Science 259:1757–1760
Zinser ER, Kolter RK (2004) Escherichia coli evolution during
stationary phase. Res Microbiol 155:328–336
Zinzer ER, Kolter R (1999) Mutations enhancing amino acid
catabolism confer a growth advantage in stationary phase.
J Bacteriol 181:5800–5807
Zinzer ER, Kolter R (2000) Prolonged stationary-phase incubation selects for lrp mutations in Escherichia coli K-12.
J Bacteriol 182:4361–4365